3.2.3. Electrical Resistivity

A two-probe measurement method was used to estimate the surface resistance as a function of the Al/(Al + Cr) ratio for arc-deposited coatings. It can be seen in Figure 8 that the electrical resistivity increases sharply with the Al portion of the metallic content in at.% [19].

**Figure 8.** Surface resistance as a function of the Al content of fcc-(Cr,Al)N and fcc-(Al,Cr)N arcdeposited coatings, redrawn after [19], original © Elsevier.

3.2.4. Poisson's Ratio, Young's Moduli, Fracture Toughness

Ab initio calculations have shown that the Poisson's ratio drops from about 0.27 for low Al contents to about 0.2 for an Al content of 70 at.% [70]. Figure 9 shows the ab initio calculated Young's moduli (E) as a function of the Al content for fcc (Al,Cr)N [70,71]. Selected Young's moduli measured by nanoindentation from [64,71] have been added.

**Figure 9.** Ab initio calculated Young's moduli E and experimentally obtained indentation moduli (black symbols) for different Al concentrations in fcc-(Cr,Al)N and fcc-(Al,Cr)N coatings, redrawn after [70], original © AIP Publishing, data from [64,71].

The Young's modulus increases with an increasing Al content. The same relative tendency, but with lower absolute values, was experimentally shown in [43]. The calculated values are in good agreement with measured nanoindentation moduli [64,72]. The Young's modulus of (AlCr)N coatings drops significantly when the mixed-phase structure fcc + hcp is reached [43], as well as for Si-alloyed (AlCr)N coatings of, for example, Al33.4Cr18.3Si2.3N46O0.7 [73]. It should be noted that large variations of measured E values for fcc-(Al,Cr)N coatings have been published for coatings of nearly the same composition, for example, from 300 GPa (Al/(Al + Cr) content of 68 at.%) [73] to 469 GPa (Al/(Al + Cr) content of 63 at.%) [71]. Different sample conditions (thickness and substrate) and measurement systems themselves will influence the measured value.

In addition to the chemical composition, the Young's modulus is also dependent on the grain size (grain boundary fraction), the compressive stress state, and the texture. A variation from 363 to 469 GPa was measured for Al28.4Cr 18.6N55 in different coating states. The high value was measured for a highly 100-oriented coating deposited on MgO (100) substrates [71]. Thus, a relatively wide variation of experimental results, besides the measuring conditions, must be anticipated.

The fracture toughness KIC of sputtered Al28.4Cr18.6N55 was measured by micromechanical bending tests at 1.3 <sup>±</sup> 0.1 MPa <sup>√</sup> m, which is lower than that of TiN at 2.0 <sup>±</sup> 0.1 MPa √ m related to domain size effects, but it is possible to raise this in a superlattice combination of the two materials [71].
